U.S. patent number 6,022,114 [Application Number 09/071,749] was granted by the patent office on 2000-02-08 for anamorphic afocal beam shaping assembly.
This patent grant is currently assigned to Nikon Corporation. Invention is credited to Leslie D. Foo.
United States Patent |
6,022,114 |
Foo |
February 8, 2000 |
Anamorphic afocal beam shaping assembly
Abstract
An anamorphic system and method having first and second
reflective anamorphic surfaces producing different magnifications
in orthogonal directions in a collimated beam of radiation incident
on the first anamorphic surface. The anamorphic surfaces have
parabolic cross-sections in the two orthogonal directions. The
parabolic cross-sections have base radii of curvatures and the
magnifications in the first and second directions are determined by
the ratio of the base radii of curvatures in the first and second
directions.
Inventors: |
Foo; Leslie D. (San Jose,
CA) |
Assignee: |
Nikon Corporation (Tokyo,
JP)
|
Family
ID: |
22103327 |
Appl.
No.: |
09/071,749 |
Filed: |
May 1, 1998 |
Current U.S.
Class: |
359/853; 359/668;
359/728; 359/858; 359/869 |
Current CPC
Class: |
G02B
27/09 (20130101); G02B 27/0911 (20130101); G02B
27/0983 (20130101) |
Current International
Class: |
G02B
27/09 (20060101); G02B 005/10 (); G02B 017/00 ();
G02B 013/08 () |
Field of
Search: |
;359/850,853,858,867,869,633,637,728,730,668 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
|
|
|
|
|
|
|
5-72477 |
|
1993 |
|
JP |
|
5-72477 |
|
Mar 1993 |
|
JP |
|
Primary Examiner: Epps; Georgia
Assistant Examiner: Lester; Evelyn A.
Attorney, Agent or Firm: Nelson; H. Donald
Claims
What is claimed is:
1. An anamorphic system comprising:
a first reflective anamorphic surface having a first aspheric
cross-section in a first direction and a second aspheric
cross-section in a second direction; and
a second reflective anamorphic surface having a third aspheric
cross-section in the first direction and a fourth aspheric
cross-section in the second direction, wherein a collimated beam of
radiation incident on the first reflective anamorphic surface is
reflected to the second reflective anamorphic surface.
2. The anamorphic system of claim 1 wherein the first aspheric
cross-section in the first direction and the third aspheric
cross-section in the first direction produce a magnification
M.sub.1 of the collimated beam of radiation in the first
direction.
3. The anamorphic system of claim 2 wherein the second aspheric
cross-section in the second direction and the fourth aspheric
cross-section in the second direction produce a magnification
M.sub.2 of the collimated beam of radiation in the second
direction.
4. The anamorphic system of claim 3 wherein M.sub.1 can be
positive, negative or one.
5. The anamorphic system of claim 4 wherein M.sub.2 can be
positive, negative or one.
6. The anamorphic system of claim 5 wherein the first aspheric
cross-section is a parabolic cross-section having a base radius of
curvature R.sub.1 and the third aspheric cross-section is a
parabolic cross-section having a base radius of curvature
R.sub.3.
7. The anamorphic system of claim 6 wherein M.sub.1 is equal to
R.sub.3 /R.sub.1.
8. The anamorphic system of claim 7 wherein the second aspheric
cross-section is a parabolic cross-section having a base radius of
curvature R.sub.2 and the fourth aspheric cross-section is a
parabolic cross-section having a base radius of curvature
R.sub.4.
9. The anamorphic system of claim 8 wherein M.sub.2 is equal to
R.sub.4 R.sub.2.
10. The anamorphic system of claim 9 wherein the second direction
is orthogonal to the first direction.
11. A method of anamorphically shaping a beam of radiation, the
method comprising directing the beam of radiation onto a first
reflective anamorphic surface having a first aspheric cross-section
in a first direction and a second aspheric cross-section in a
second direction wherein the beam of radiation is reflected by the
first reflective anamorphic surface to a second reflective
anamorphic surface having a third aspheric cross-section in the
first direction and a fourth aspheric cross-section in the second
direction.
12. The method of claim 11 further comprising producing a
magnification M.sub.1 of the beam of radiation in the first
direction wherein the magnification M.sub.1 is produced by the
first aspheric cross-section and the third aspheric
cross-section.
13. The method of claim 12 further comprising producing a
magnification M.sub.2 of the beam of radiation in the second
direction wherein the magnification M.sub.2 produced by the second
aspheric cross-section and the fourth aspheric cross-section.
14. The method of claim 13 wherein the produced magnification
M.sub.1 can be positive, negative or one.
15. The method of claim 14 wherein the produced magnification
M.sub.2 can be positive, negative or one.
16. The method of claim 15 wherein the first aspheric cross-section
is a parabolic cross-section having a base radius of curvature
R.sub.1 and the third aspheric cross-section is a parabolic
cross-section having a base radius of curvature R.sub.3.
17. The method of claim 16 wherein the produced magnification
M.sub.1 is equal to R.sub.3 /R.sub.1.
18. The method of claim 17 wherein the second aspheric
cross-section is a parabolic cross-section having a base radius of
curvature R.sub.2 and the fourth aspheric cross-section is a
parabolic cross-section having a base radius of curvature
R.sub.4.
19. The method of claim 18 wherein the produced magnification
M.sub.2 equal to R.sub.4 /R.sub.2.
20. The method of claim 19 wherein the second direction is
orthogonal to the first direction.
Description
FIELD OF THE INVENTION
This invention relates generally to an apparatus and method for
producing a uniformly illuminated area having a desired shape. More
specifically, this invention relates to an anamorphic afocal beam
shaping apparatus and method for producing a uniformly illuminated
area having a desired shape, minimum optical aberrations, a
non-obscured output beam and high efficiency. Even more
specifically, this invention relates to an anamorphic afocal beam
shaping apparatus and method using off-axis segments of parent
anamorphic surfaces.
BACKGROUND OF THE INVENTION
When collimated (parallel) radiation is incident upon the input of
a lens system, radiation exiting from the output end will show one
of three characteristics: (1) it will converge to a real point
focus outside the lens system, (2) it will appear to diverge from a
virtual point focus within the lens system, or (3) it will emerge
as collimated radiation that may differ in some characteristics
from the incident collimated radiation. In cases 1 and 2, the
paraxial imaging properties of the lens system can be modeled
accurately by a characteristic focal length and a set of fixed
principal surfaces. Such lens systems are sometimes referred to as
focusing or focal lenses, however they are usually referred to
simply as lenses. In case 3, a single finite focal length cannot
model the paraxial characteristics of the lens system; in effect,
the focal length is infinite, with the output focal point an
infinite distance behind the lens, and the associated principal
surface an infinite distance in front of the lens. Such lens
systems are referred to as "afocal," or without focal length. They
are referred to as "afocal lenses," following the common practice
of using "lens" to refer to both single element and multi-element
lens systems.
A simple afocal lens can be made up of two focusing lenses set up
so that the rear focal point of the first lens coincides with the
front focal point of the second lens. There are two general classes
of simple afocal lenses, one in which both focusing lenses are
positive, and the other in which one of the two is negative. Afocal
lenses containing two positive lenses were first described by
Johannes Kepler and are called Keplerian. Afocal lenses containing
a negative lens are called Galilean. Generally, afocal lenses
contain at least two powered surfaces, with the simplest model for
an afocal lens consisting of two thin lenses.
The combination of a first lens having a positive refractive power
(the "first" lens being the lens nearest the object) and a second
lens having a negative refractive power is a Galilean
configuration. The combination with the first lens having a
negative refractive power and the second lens having a positive
refractive power is referred to as an inverse Galilean
configuration.
Afocal attachments to lens systems can compress or expand the scale
or shape of an image in one axis. Such devices are called
"anamorphosers," or "anamorphic afocal attachments." One class of
anamorphoser is the cylindrical galilean telescope. The keplerian
form is seldom if ever used, since a cylindrical keplerian
telescope would introduce image inversion in one direction.
Anamorphic compression can also be obtained using two prisms.
There are increasing requirements for illumination systems that can
provide anamorphic beam shaping. One such requirement is in the
field of photolithography in which illumination of a
non-symmetrical area with collimated energy is needed. Another such
requirement is in the field of laser beam shaping in which, for
example, there is a need to shape the elliptical output from a
semiconductor diode laser into a desired circular output shape.
Another requirement is to provide beam shaping in those spectral
regions in which there are no refractive materials appropriate for
the energy in those spectral regions, for example x-ray
applications.
A current method of producing an illuminated area having a desired
shape is shown in FIG. 1 in which a collimated beam 102 having a
power P.sub.IN illuminates a mask 104 with an aperture 106 having
the shape of the desired illuminated area 100. The illuminated area
100 has a power P.sub.OUT that is less than P.sub.IN and P.sub.OUT
depends upon the size of the aperture 106 relative to the size of
the input collimated beam 102. This method is satisfactory if
efficiency is not a problem or concern in the system. The
efficiency .eta.=P.sub.OUT /P.sub.IN where P.sub.OUT is the power
in the output beam 100 and P.sub.IN is the power in the input beam
102. As can be appreciated the efficiency can be very low.
Another method of providing a scaled or shaped beam has been to use
prisms or cylindrical lenses to provide anamorphic scaling of input
beams. Such an anamorphic system 200 is shown in FIG. 2. The
anamorphic system 200 has a positive cylindrical lens element 202
and a negative cylindrical lens element 204 to shape an incoming
beam 206 into an anamorphic output beam 208. The efficiency .eta.
of such a system is P.sub.OUT /P.sub.IN where P.sub.OUT is the
power in the output beam 208 and P.sub.IN is the power in the input
beam 206. Assuming there is no transmission loss in the lens
elements, the efficiency .theta..apprxeq.1. However, the lens
option is limited to spectral regions for which there are
refractive materials available to construct cylindrical lenses or
prisms. In addition, if the input beam is broad band, the lens
assembly introduces chromatic aberration.
FIG. 3 shows a mirror equivalent 300 to the anamorphic system 200
shown in FIG. 2. An input beam 302 is incident on Mirror, 304, and
then on Mirror.sub.2 306. To obtain anamorphic shaping, a surface
of Mirror.sub.1 304 and Mirror.sub.2 306 are cylindrical. The
output beam 308 is shown rotated 90.degree. for illustrative
purposes and indicates anamorphic scaling of the output beam 308.
When the system is configured having a common axis as shown in FIG.
3, the output beam 308 has the central region 310 obscured because
of Mirror.sub.1 304. The obscuration 310 is the shadow of
Mirror.sub.1 304.
The prior art systems discussed above either have low efficiency,
exhibit optical aberrations or have an obscured output beam.
Accordingly, there is a need for an apparatus and method for
producing an afocal, uniformly illuminated area having a desired
shape with high transmission efficiency and minimum optical
aberrations.
SUMMARY OF THE INVENTION
According to the present invention, the foregoing and other
advantages are attained by an anamorphic system and method having
first and second reflective anamorphic surfaces. The reflective
anamorphic surfaces produce different magnifications is orthogonal
directions in a beam of collimated radiation. In one aspect of the
invention the anamorphic surfaces have parabolic cross-sections
with base radii of curvatures. The magnification of the beam in
each direction is determined by the ratio of the radii of the
parabolic cross-sections in each direction in the first and second
anamorphic surfaces.
These and other advantages of the present invention will become
more apparent upon a reading of the detailed description of the
preferred embodiment or embodiments that follow, when considered in
conjunction with the drawings of which the following is a brief
description. It should be clear that the drawings are merely
illustrative of the currently preferred embodiment of the present
invention, and that the invention is in no way limited to the
illustrated embodiments. As will be realized, the invention is
capable of other embodiments and its several details are capable of
modifications in various obvious aspects, all without departing
from the scope of the invention. The present invention is best
defined by the claims appended to this specification.
BRIEF DESCRIPTION OF THE DRAWINGS
The novel features believed characteristic of the invention are set
forth in the appended claims. The invention itself, however, as
well as a preferred mode of use, and further objects and advantages
thereof, will best be understood by reference to the following
detailed description of illustrative embodiments when read in
conjunction with the accompanying drawings, wherein:
FIG. 1 illustrates a prior art apparatus for obtaining a shaped
beam by illuminating an aperture in a mask;
FIG. 2 illustrates a prior art apparatus for obtaining a shaped
beam by using cylindrical lens element to obtain anamorphic scaling
of an input beam;
FIG. 3 illustrates a prior art mirror equivalent of the apparatus
shown in FIG. 2;
FIG. 4 shows the relationships of the parameters defining a conic
surface;
FIG. 5A is a side view of an anamorphic system in accordance with
the present invention;
FIG. 5B is a top view of the anamorphic system shown in FIG.
5A;
FIG. 6 is a side view of an anamorphic system having parabolic
cross-sections;
FIG. 7 is a top view of the anamorphic system shown in FIGS. 6;
FIG. 8 is a perspective view of the anamorphic system shown in
FIGS. 5 & 6;
FIG. 9A shows a Keplerian lens configuration in a beam expander
configuration;
FIG. 9B shows a Keplerian lens configuration in a beam compressor
configuration;
FIG. 9C shows a Galilean lens configuration in a beam compressor
configuration;
FIG. 9D shows a Galilean lens configuration in a beam expander
configuration;
FIG. 10A illustrates a reflective anamorphic system having a
Keplerian configuration in the y direction and a Galilean
configuration in the x direction;
FIG. 10B shows the input and output beam shapes for the system
shown in FIG. 10A;
FIG. 11A illustrates an anamorphic mirror system having a Keplerian
configuration in the y direction and a Keplerian configuration in
the x direction;
FIG. 11B shows the input and output beam shapes for the system
shown in FIG. 11A;
FIG. 12A illustrates an anamorphic mirror system having a Galilean
configuration in the y direction and a Keplerian configuration in
the x direction;
FIG. 12B shows the input and output beam shapes for the system
shown in FIG. 12A;
FIG. 13A illustrates an anamorphic mirror system having a Galilean
configuration in the y direction and a Galilean configuration in
the x direction; and
FIG. 13B shows the input and output beam shapes for the system
shown in FIG. 13A.
DETAILED DESCRIPTION
The following detailed description is of the presently preferred
embodiments of the present invention. It is to be understood that
while the detailed description is given utilizing the drawings
briefly described above, the invention is not limited to the
illustrated embodiments. In the detailed description, like
reference numbers refer to like elements.
FIG. 4 shows an aspheric surface with bilateral symmetry in both
the x direction and the y direction but not necessarily having
rotational symmetry. The curve S.sub.y 400 is an aspheric curve in
the y-z plane. The curve S.sub.x 402 is an aspheric curve in the
x-z plane. The point P 404 is on the curve S.sub.y 406. The curve
S.sub.y 402 is characterized by a base radius of curvature R.sub.y
and the curve S.sub.x is characterized by a base radius of
curvature R.sub.x. The curvature C.sub.y the curve S.sub.y is
1/R.sub.y and the curvature C.sub.x of the curve S.sub.x 402 is
1/R.sub.x. The value z 408 is the sag (the distance of the point P
404 from the y-x plane 410). The sag z 408 is calculated as
follows:
where K.sub.y and K.sub.x are the conic coefficients in x and y,
respectively, and correspond to eccentricity in the same way as K
for the asphere surface type and have the following values:
______________________________________ k = 0 sphere -1 < k <
0 ellipsoid with major axis on the optical axis (prolate spheroid)
k = -1 paraboloid k < -1 hyperboloid
______________________________________
Also, k=-e.sup.e, where e is eccentricity. For
______________________________________ k > 0 oblate spheroid
(not a conic section) the surface is generated by rotating an
ellipse about its minor axis and
______________________________________
k=e.sup.2 /(1-e.sup.2), where e is the eccentricity of the
generating ellipse.
FIG. 5A is a side view of a reflective anamorphic system 500 that
produces an afocal, non-obscured beam with no optical aberration.
An anamorphic system provides anamorphic magnification, which is
defined as different magnification of the image in each of two
orthogonal directions. The reflective anamorphic system 500
includes Mirror.sub.1 502 and Mirror.sub.2 504. The surface 506
defined by the y-z plane of Mirror.sub.1 502 and the surface 508
defined by the y-z plane of Mirror.sub.2 504 each have parabolic
cross-sections in the respective planes. Mirror.sub.1 502 and
Mirror.sub.2 504 are off-axis portions of anamorphic surfaces. In
orthogonal directions, the anamorphic surfaces 506 and 508 have
parabolic cross sections, either concave or convex. The mirrors 502
and 504 have common foci in their respective planes. Mirror.sub.1
502 has a parabolic cross-section in the y-z plane. R.sub.1y is the
base radius of curvature of the parabolic cross-section of surface
506 in the y-z plane and K.sub.1y is a conic constant of the
parabolic cross-section of the surface 506 in the y-z plane and
K.sub.1y =-1. Mirror.sub.2 504 also has a parabolic cross-section
in the y-z plane. R.sub.2y is the base radius of curvature of the
parabolic cross-section of the surface 508 in the y-z plane and
K.sub.2y is a conic constant of the parabolic cross-section of the
surface 508 in the y-z plane. If R.sub.2y =R.sub.1y, the
magnification in the y direction is M.sub.y =R.sub.2y /R.sub.1y =1.
With a magnification M.sub.y =1, the outgoing beam 510 will have
the same dimension in the y-z plane as the incoming beam 512.
FIG. 5B illustrates the top view of the reflective anamorphic
system 500 shown in FIG. 5A. The surface 506 defined by the x-z
plane of Mirror.sub.1 502 and the surface 508 defined by the x-z
plane of Mirror.sub.2 504 each have parabolic cross-sections in the
respective planes. R.sub.1x is the base radius of curvature of the
surface 506 in the x-z plane and K.sub.1x is a conic constant of
the parabolic cross-section of the surface 506 in the x-z plane and
K.sub.1x =-1. R.sub.2x is the base radius of curvature of the
surface 508 in the x-z plane and K.sub.2x is the conic constant of
parabolic cross-section of the surface 508 and K.sub.2x =-1.
R.sub.2x =2(D+.sub.fx) where D is the axial distance 514 between
surface 506 of Mirror.sub.1 502 and surface 508 of Mirror.sub.2 504
and f.sub.x is the axial focal length 516 of Mirror.sub.2 in the
x-z plane. The magnification M.sub.x in the x direction=f.sub.2x
/f.sub.1x =R.sub.2x /R.sub.1x =2(D+f.sub.x)/R.sub.1x. Since
Mirror.sub.1 502 and Mirror.sub.2 504 have parabolic cross-sections
in orthogonal directions, they produce foci with no aberrations
when illuminated with collimated radiation that propagates along
the common optical axis 518 of the two mirrors 502 and 504. This is
similar to the afocal Cassegrain-Mersenne telescope configuration,
which is composed of two confocal paraboloids working at infinite
conjugates and is an afocal system with magnification. In such a
system, all third order aberrations, except field curvature, are
corrected by surfaces that have parabolic cross-sections. Because
there are no refractive elements, the all-reflective aspect of the
reflective anamorphic system 500 is well suited for applications
for which there are no suitable refractive materials, such as
applications using x-rays.
FIG. 6 is a side view of a reflective anamorphic system 600 having
mirror surfaces with parabolic cross-sections in orthogonal
directions to provide anamorphic magnification. The anamorphic
system 600 includes Mirror.sub.1 602 having a surface 604, which
has a reflective concave parabolic cross-section of the anamorphic
surface 604 in the y-z direction. R.sub.1y is the base radius of
curvature of the parabolic cross-section of the anamorphic surface
604 in the y-z direction. K.sub.1y is a conic constant of the
parabolic cross-section of the anamorphic surface 406 in the y-z
plane. The anamorphic system also includes Mirror.sub.2 606 having
a surface 608, which is a reflective concave parabolic
cross-section of the anarnorphic surface 604 in the y-z direction.
R.sub.2y is the base radius of curvature of the parabolic
cross-section of the anamorphic surface 608 in the y-z direction.
K.sub.2y is a conic constant of the parabolic cross-section of the
anamorphic surface 608 in the y-z plane. A collimated beam of
radiation 610 is incident on the anamorphic surface 604 and is
reflected to the reflective anamorphic surface 608 where it is
reflected as a collimated beam 612. The collimated beam of
radiation 610 shown in FIG. 6 represents the portion of the
radiation in the y plane. The line 611 on the surface 604 is the
apex of the convex parabolic cross-section of the anamorphic
surface 604. The line 613 is the bottommost or nadir of the
anamorphic surface 608.
FIG. 7 is the top view of the reflective anamorphic system 600
shown in FIG. 6. The surface 604 defined by the x-z plane of
Mirror.sub.1 602 and the surface 608 defined by the x-z plane of
Mirror.sub.2 606 each have parabolic cross-sections in the
respective planes. R.sub.1x is the base radius of curvature of the
parabolic cross-section of the anamorphic surface 604 in the x-z
direction. K.sub.1x is a conic constant of the parabolic
cross-section of the anamorphic surface 604 in the x-z direction.
R.sub.2x is the base radius of curvature of the parabolic
cross-section of the anamorphic surface 608 in the x-z direction.
K.sub.2x is a conic constant of the parabolic cross-section of the
anamorphic surface 608 in the x-z direction. Mirror.sub.1 602 and
Mirror.sub.2 606 have surfaces 604 and 608 respectively, each of
which is based upon an off-axis portion of an anamorphic surface.
The dotted line 614 is an intermediate portion of the surface 604
indicating where a central horizontal portion of the beam of
radiation would strike the surface 604. Similarly, the line 618 is
an intermediate portion of the surface 608. The input beam 610
shown in FIG. 7 represents radiation in the x-z plane incident on
the surface 604. The output beam 612 represents radiation in the
x-z plane output from the surface 608.
FIG. 8 is a perspective view of the reflective anamorphic system
600 shown in FIGS. 6 & 7. The dotted box 620 shows the shape of
the incoming collimated beam 610 showing 5 ray incidence points
that are incident on surface 604 of Mirror.sub.1. There is shown a
vertical grouping of points 622 in the y direction and a horizontal
grouping or points 624 in the x direction. The dotted box 626 shows
the outgoing shape of the collimated beam 612 showing the 5 ray
incidence points leaving the anamorphic system 600. The grouping of
points 628 in the y direction are shown having the same vertical
separation indicating no magnification in the y direction. The
grouping of points 630 in the x direction are shown expanded
indicating a positive magnification in the x direction. An example
of the utility of this invention can be observed by assuming that
R.sub.1y =4, K.sub.1y =-1, R.sub.2y =4 and K.sub.2y =-1. Then the
beam scaling or magnification in the y direction R.sub.2y /R.sub.1y
=4/4=1. If R.sub.1x =4, K.sub.1x =-1, R.sub.2x =12 and K.sub.2x
=-1, then the beam scaling or magnification in the x
direction=R.sub.2x /R.sub.1x =12/4=3. This gives a 3:1 aspect ratio
(x:y)from the original 1:1 aspect ratio.
FIGS. 9A-D illustrate how Keplerian and Galilean lens
configurations are used to shape an incoming beam by expanding or
magnifying (positive magnification) the beam or by compressing or
de-magnifying (negative magnification) the beam.
FIG. 9A shows two positive lens elements 900 and 902 in a Keplerian
configuration to expand an incoming collimated beam of radiation
904 to an extent depending upon the relative powers of the lens
elements 900 and 902.
FIG. 9B shows two positive lens elements 906 and 908 in a Keplerian
configuration to de-magnify or compress an incoming collimated beam
910 of radiation to an extent depending upon the relative powers of
the lens elements 906 and 908.
FIG. 9C shows a positive lens element 912 and a negative lens
element 914 in a Galilean configuration to de-magnify or compress
an incoming collimated beam of radiation 916 to an extent depending
upon the relative powers of the lens elements 912 and 914.
FIG. 9D shows a negative lens element 918 and a positive lens
element 920 in a Galilean configuration to magnify or expand an
incoming collimated beam of radiation 922 to an extent depending
upon the relative powers of the lens elements 918 and 920.
FIGS. 10A-13B show how beam scaling or shaping can be obtained with
the use of anamorphic mirror segments in Keplerian configurations,
Galilean configurations or combinations of Keplerian and Galilean
configurations.
FIG. 10A shows a reflective anamorphic system 1000 with a Keplerian
configuration 1002 of reflective surfaces having parabolic
cross-sections in the y-z plane and a Galilean configuration 1004
of reflective surfaces having parabolic cross-sections in the x-z
plane. The Keplerian configuration 1002 has a reflective surface
1006 having a positive (concave) parabolic cross-section in the y-z
plane and a reflective surface 1008 having a positive parabolic
cross-section in the y-z plane. The magnification of the collimated
beam 1010 in the y direction is determined by the values of the
base radii of curvature of the parabolic cross-sections of the
surfaces 1006 and 1008 in the y-z plane. The Galilean configuration
1004 has a reflective surface 1012 having a negative (convex)
parabolic cross-section in the x-z plane and a reflective surface
1014 having a positive parabolic cross-section in the x-z plane.
The magnification of the collimated beam 1110 in the x direction is
determined by the values of the base radii of curvature of the
parabolic cross-sections of the surfaces 1012 and 1014 in the x-z
plane.
FIG. 10B shows an incoming circular beam of radiation 1018 and the
outgoing elliptical beam of radiation 1020 after it has been
expanded or magnified in the x direction by the Galilean
configuration of reflective surfaces 1012 and 1014 in the x-z plane
shown in FIG. 10A. Also shown is an incoming elliptical beam of
radiation 1022 and the outgoing circular beam of radiation 1024
after it has been expanded or magnified in the x direction by the
Galilean configuration of reflective surfaces 1012 and 1014 in the
x-z plane shown n FIG. 10A. The beam shaping capability of the
anamorphic system 1000 is evident from these examples.
FIG. 11A shows a reflective anamorphic system 1026 with a Keplerian
configuration 1028 of reflective surfaces having parabolic
cross-sections in the y-z plane and a Keplerian configuration 1030
of reflective surfaces having parabolic cross-sections in the x-z
plane. The Keplerian configuration 1028 has a reflective surface
1030 having a positive parabolic cross-section in the y-z plane and
a reflective surface 1032 having a positive parabolic cross-section
in the y-z plane. The magnification of the collimated beam 1034 in
the y direction is determined by the values of the base radii of
curvature of the parabolic cross-sections of the surfaces 1031 and
1032 in the y-z plane. The Keplerian configuration 1030 has a
reflective surface 1036 having a positive parabolic cross-section
in the x-z plane and a reflective surface 1038 having a positive
parabolic cross-section in the x-z plane. The magnification of the
collimated beam 1034 in the x direction is determined by the values
of the base radii of curvature of the parabolic cross-sections of
the surfaces 1036 and 1038 in the x-z plane.
FIG. 11B shows an incoming circular beam of radiation 1040 and the
outgoing circular beam of radiation 1042 after it has been expanded
or magnified in the y direction by the Keplerian configuration of
reflective surfaces 1030 and 1032 in the y-z plane and after it has
been expanded or magnified in the x direction by the Keplerian
configuration of reflective surfaces 1036 and 1038 in the x-z
plane.
FIG. 12A shows a reflective anamorphic system 1044 with a Galilean
configuration 1046 of reflective surfaces having parabolic
cross-sections in the y-z plane and a Keplerian configuration 1048
of reflective surfaces having parabolic cross-sections in the x-z
plane. The Galilean configuration 1046 has a reflective surface
1050 having a negative parabolic cross-section in the y-z plane and
a reflective surface 1052 having a positive parabolic cross-section
in the y-z plane. The magnification of the collimated beam 1054 in
the y direction is determined by the values of the base radii of
curvature of the parabolic cross-sections of the surfaces 1050 and
1052 in the y-z plane. The Keplerian configuration 1048 has a
reflective surface 1056 having a positive parabolic cross-section
in the x-z plane and a reflective surface 1058 having a positive
parabolic cross-section in the x-z plane. The magnification of the
collimated beam 1054 in the x direction is determined by the values
of the base radii of curvature of the parabolic cross-sections of
the surfaces 1056 and 1058 in the x-z plane.
FIG. 12B shows an incoming circular beam of radiation 1060 and the
outgoing elliptical beam of radiation 1062 after it has been
expanded in the y direction by the Galilean configuration of
reflective surfaces 1050 and 1052 in the y-z plane shown in FIG.
12A. Also shown is an incoming elliptical beam of radiation 1064
and the outgoing circular beam of radiation 1066 after it has been
expanded in the y direction by the Galilean configuration of
reflective surfaces 1050 and 1052 in the y-z plane shown in FIG.
12A.
FIG. 13A shows a reflective anamorphic system 1068 with a Galilean
configuration 1070 of reflective surfaces having parabolic
cross-sections in the y-z plane and a Galilean configuration 1072
of reflective surfaces having parabolic cross-sections in the x-z
plane. The Galilean configuration 1070 has a reflective surface
1074 having a negative parabolic cross-section in the y-z plane and
a reflective surface 1076 having a positive parabolic cross-section
in the y-z plane. The magnification of the collimated beam 1078 in
the y direction is determined by the values of the base radii of
curvature of the parabolic cross-sections of the surfaces 1074 and
1076 in the y-z plane. The Galilean configuration 1072 has a
reflective surface 1080 having a negative parabolic cross-section
in the x-z plane and a reflective surface 1082 having a positive
parabolic cross-section in the x-z plane. The magnification of the
collimated beam 1078 in the x direction is determined by the values
of the base radii of curvature of the parabolic cross-sections of
the surfaces 1080 and 1082 in the x-z plane. FIG. 13B shows an
incoming circular beam of radiation 1084 and the outgoing circular
beam of radiation 1086 after it has been expanded or magnified in
the y direction by the Galilean configuration of reflective
surfaces 1074 and 1076 in the y-z plane shown in FIG. 13A and after
it has been expanded or magnified in the x direction by the
Galilean configuration of reflective surface 1080 and 1082 in the
x-z plane shown in FIG. 13A.
In summary, the results and advantages of the anamorphic system and
method of the present invention can now be more fully realized. The
first and second reflective anamorphic surfaces provide beam
shaping and scaling of a beam of radiation incident on the first
reflective anamorphic surface. The first and second reflective
anamorphic surfaces have parabolic cross-sections in orthogonal
directions with the magnifications in the first and second
directions determined by the base radii of curvatures of the
parabolic cross-sections in the first and second directions. The
method and apparatus can be utilized for applications in spectral
regions that do not have appropriate refractive materials such as
x-ray applications.
The foregoing description of the embodiment of the invention has
been presented for purposes of illustration and description. It is
not intended to be exhaustive or to limit the invention to the
precise form disclosed. Obvious modifications or variations are
possible in light of the above teachings. The embodiment was chosen
and described to provide the best illustration of the principles of
the invention and its practical application to thereby enable one
of ordinary skill in the art to utilize the invention in various
embodiments and with various modifications as are suited to the
particular use contemplated. All such modifications and variations
are within the scope of the invention as determined by the appended
claims when interpreted in accordance with the breadth to which
they are fairly, legally, and equitably entitled.
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